While mozzarella is cold, slice it into 1/4-inch slices.
Let it sit, loosely covered, to come to room temperature while you prepare the tomatoes.
Slice the tomatoes into 1/4-inch to 1/2-inch thick wedges, leaving them in a single layer on the cutting board as you go.
Sprinkle generously with salt.
On a serving platter, arrange the mozzarella, tomato slices, and whole basil leaves so they overlap slightly.
Pour any tomato juices from the cutting board over the dish.
Sprinkle again with salt and pepper, and drizzle with plenty of oil.
Top with reserved basil, and serve.
